Interferometers are widely used for characterizing optical elements and systems. Two-beam interferometers split a single coherent optical beam into two beams that travel along separate paths. One beam is used as an object beam that is altered by the test element or system. The other beam is used as a reference beam, which is not transmitted through the system, and retains its original wavefront shape. Recombining the two beams creates an intensity pattern (interferogram) resulting from constructive and destructive superposition of the beams. This interferogram can be analyzed to determine information about the element or system in test. However, such two-beam interferometers are difficult to align and environmentally unstable.
Phase-shifting interferometers shift the phase between the object and reference beams to provide more information about the properties of the optical element or system. As more fully described in a paper, “Phase-Shifting Scatterplate Interferometer,” by North-Morris et al., Advanced Optical Manufacturing and Testing Technology, Proceedings of SPIE, Vol. 4231, pp. 59–65, 2000, (“the North-Morris paper”) in phase shifting interferometry a series of interferograms are recorded while the reference phase is changed. Alternatively, the object phase may be changed. The resulting changes in the interferogram can be used to better characterize the object beam and therefore the system from which it originated. However, generating the phase shift usually adds a level of complexity to the interferometer system.
In common-path interferometers the object and reference beams travel along a common path. When the two beams travel along the same path the interferometer is more environmentally stable because vibration, thermal effects, noise, and other limiting environmental factors are the same for the two beams. Introducing phase shifts between coincident object and reference beams, however, has been difficult because of the need to optically distinguish between the two beams traveling along the same path.
Point diffraction interferometers (PDI) are a kind of common-path interferometer, as described in an article, “Point-Diffraction Interferometer,” by R. N. Smartt and J. Strong, Journal of the Optical Society of America, 62, p. 737, (1972). The Smartt et al. PDI is illustrated in FIGS. 1a and 1b. Transparent substrate 10 is coated with semi-transparent coating 12 except for pinhole-sized region 14 that is left uncoated. Pinhole-sized region 14 is on the order of a few microns in diameter and is circular in shape. Uncoated pin-hole sized region 14 acts as a diffractive feature, similar to a pinhole aperture. The beam under test 16 is brought to a focus 18 using lens 20 at a position near the diffractive feature, pin-hole sized region 14. A portion of beam 16 is thereby transmitted though the diffractive feature, pin-hole sized region 14 and generates a substantially spherical wavefront for reference beam 22, in accordance with Huygens' Principle. The remaining portion of impinging beam 16 under test is transmitted through coated substrate 10 in the region adjacent pinhole-sized region 14, retaining the original wavefront shape of beam under test 16, but attenuated by semi-transparent coating 12. This remaining portion becomes object beam 24. Object beam 24 and reference beam 22 now travel along the same path, or in coincidence. In accordance with the principle of superposition, object beam 24 and reference beam 22, now produce an intensity pattern 26 resulting from constructive and destructive interference of the beams. The interfering beams are then imaged onto image plane 28 with lens 30. In order to form interferograms with maximized contrast it is important to have the individual intensities of reference beam 22 and object beams 24 nearly equal. Therefore, the amount of attenuation that is introduced by semi-transparent coating 12 is often tailored so that each beam has nearly equal intensity.
Diffraction provides a nearly perfect spherical beam, and the diffractive feature pinhole-sized region 14, allows for the creation of a spherical reference beam exceeding the accuracy available from a two-beam interferometer. In order to form the best spherical beam for the reference beam, C. Kiliopoulous et al. showed that pinhole-sized region 14 should have a dimension less than the diameter of the spot formed, airy disk, from focused beam 16, as described in a paper, “Infrared Point-Diffraction Interferometer,” Optical Letters 3, pp. 118–120, (1978).
Improving on the PDI, Mercer developed a liquid crystal point-diffraction interferometer (LCPDI), as described in U.S. Pat. No. 5,689,314 (“the '314 patent”, and as shown in FIGS. 2a and 2b. The LCPDI uses the phase shifting properties of liquid crystal cells. This interferometer employs optical beam 40 that is polarized by linear polarizer 42. Lens 44 images the optical beam onto focal point 46 adjacent to liquid crystal cell 48. The latter consists of glass microsphere 50 within layer of liquid crystals 52 that is sandwiched between glass substrates 54a, 54b with transparent conductive coatings 56a, 56b (see FIG. 2b). Optical properties of liquid crystal layer 52 are controlled by voltage source 58 applied across transparent conductive coatings 56a, 56b. The portion of optical beam 40 traveling through microsphere 50 creates a reference beam 60 with a substantially spherical wavefront, while the remainder of optical beam 40 is transmitted through layer of liquid crystals 52 adjacent microsphere 50 as object beam 62. Application of a voltage to liquid crystal cell 48 creates an electric field within liquid crystal layer 52. This electric field orients the liquid crystal molecules such that the optical path of object beam 62 is altered, shifting the phase of object beam 62 with respect to reference beam 60 whose optical path is unaffected by the voltage. Reference beam 60 undergoes no phase shifting, as it never travels through liquid crystal layer 52. Interfering reference beam 60 and object beam 62 are then imaged using lens 64 onto image plane 66 where they form interferogram 68.
One limitation of the device of the '314 patent arises from local distortion of the liquid crystals due to molecular anchoring affects at the surface of microsphere 50. Another limitation is that dyes must be added to liquid crystals 52 in order to attenuate intensity of object beam 62. Modulation of liquid crystal layer 52 changes the orientation of the dye molecules, which changes their attenuation. The saturation limit of this dye mixture also limits how thin liquid crystal cell 48 can be manufactured, and this limits the speed at which the phase relationship between reference beam 60 and object beam 62 can be modulated, limiting its use in fast changing dynamic systems. The complex diffractive structure created by microsphere 50 embedded in liquid crystals is likely to cause distortion in reference beam 60, limiting how close to a perfect spherical wavefront it can produce.
Polarization techniques have been used to optically distinguish between the object and reference beams. In U.S. Pat. No. 5,933,236, Sommargren uses a half wave retardation plate to produce two orthogonally polarized beams which are then split by a polarization beam splitter so the horizontal polarization is transmitted while the vertical polarization is reflected so the two beams travel along the two arms of a two-beam interferometer.
The North-Morris paper discusses the use of polarization in conjunction with a quarter wave plate with scattering features in order to form phase-shifted interferograms in a common-path interferometer, as shown in FIG. 3. This interferometer includes source of light 80 which is focused by lens 82 and reflected from mirror 84 onto ground glass plate 86, which is used to reduce speckle, as shown in FIG. 3. Light transmitted through ground glass plate 86 is then transmitted through lens 88, polarizer 90 and liquid crystal phase modulator 92. The light is then reflected with beam splitter 94 through scatter plate 96 and calcite quarter wave plate 98. Portion 100 of the light from calcite quarter wave plate 98 is transmitted and comes to focus 102 on test mirror 104. The remainder of light from calcite quarter wave plate 98 is scattered 106 and is reflected off test mirror 104. Beam 100 and beam 106 are reflected by test mirror 104 back through quarter wave plate 98, scatterplate 96 and beam splitter 94. Lens 108 is used to direct the reflected beams through analyzer 110 and image the resulting interferogram onto CCD array 112. This interferometer is limited to the testing of mirror 104 from which beams 100 and 106 are both reflected. In addition, the double-pass nature of the interferometer creates a “hot spot” in the center of the interferogram, which does not allow all of the interferogram to be used in gathering test system data. Furthermore, the light that is scattered by both the first and the second passes of the scatterplate contributes to background noise in the interferogram.
In another interferometer, U.S. Pat. No. 6,304,330 B1, a plurality of phase-shifted interferograms are generated simultaneously. This is accomplished with the use of a holographic optical element (HOE), used to divide an incident wavefront into four discrete sub-wavefronts. A method is provided for introducing a phase shift between orthogonally polarized reference and object wavefronts that is uniform across each sub-wavefront and not sensitive to the positioning of the HOE. The interferometer described uses two separate paths in order to generate a reference wave, dissimilar to the object wave, and introduce a polarization difference between the two waves. This interferometer has the disadvantage of requiring two paths in order to generate the necessary object and reference waves with orthogonal polarizations. By relying on two independent optical paths, further disadvantages are introduced such as the requirement of strict environmental controls, a source with a long coherence length, and a high-quality reference surface.
As noted above, current common-path, phase-shifting interferometers each suffer from deficiencies that limit their use and functionality. Thus, a better system for phase-shifting, common-path interferometers is needed that is diverse in application, can provide nearly perfect reference beams, and can provide interferograms with unity contrast.